Linear Regression

What this tool actually does

For educational and research purposes. It provides statistical calculations using ordinary least squares regression, with the usual summary statistics, variance inflation factors and residual plots. Results should be validated using professional statistical software.

Assumptions not checked

This tool does not verify linearity, normality, homoscedasticity, independence or multicollinearity. Violating these assumptions may invalidate results, and the page will print a confident answer either way.

• Independence is the one that quietly ruins standard errors. Time series, repeated measures, clustered or spatially correlated data break the iid error assumption, so the reported standard errors, confidence intervals and p-values are wrong, usually far too small.
• R² measures fit, not correctness. Anscombe's quartet is four datasets with the same regression line and the same R², only one of which should be fitted with a line. Read the residual plot before the summary statistics.
• Influential points. A single high-leverage observation can set the slope. Nothing here reports Cook's distance or leverage, so look at the scatter.
• Variance inflation factors flag collinearity, they do not fix it. A high VIF means the individual coefficients are not separately interpretable, even when the model predicts well.
• Extrapolation. The fit describes the range of the data. Outside it, the line is an assumption, not a result.

What a p-value here does not mean

• It assumes the model and the sampling design were fixed before you saw the data. Choosing predictors by looking at this page and then reading the p-values is not a hypothesis test.
• It carries no correction for multiple comparisons. Fit enough specifications and something will clear 0.05.
• It says nothing about effect size, practical importance, or whether the relationship is causal. A regression coefficient is not a causal effect, however small the p-value is.

No professional advice

Consult a statistician for research design, hypothesis testing and interpretation. This tool is not a substitute for professional statistical analysis. Never use it for:

• Clinical, epidemiological or medical inference, or any analysis a diagnosis or treatment rests on.
• Regulatory submissions and pre-specified statistical analysis plans.
• Financial, actuarial or risk modelling used to price, allocate or underwrite.
• Forensic or legal evidence.
• Published research, without a statistician and an analysis plan set before the data were seen.
• Decisions about people, including hiring, credit, insurance or benefits, where a fitted coefficient becomes a policy.